Question

Hillary stands directly in front of speaker S1 and walks straight away (down on the page) What is the first distance (measured from S1) at which she will hear minimum loudness? Speed of sound is 341 m/s and the frequency of the sound is 496 Hz. The speakers are 2.07 m apart.

no idea how to do this. any guidance would be greatly appreciated.

Answer 1

calculate wavelength
l (wavelength)
V=fl l=341/496=0.6875m
min loudness (out of phase) L/2=0.3438m

using triangles,
b^2=x^2+2.07^2

(let x be the distance hillary walked and b the distance from the farther speaker to Hillary's present position facing the close speaker)

we now derive another equation to be able to solve
we know that delta d we just solved for is the difference in position of the speakers with reference to Hillary.

b-x= 0.3438......(2)
b^2-x^2=4.285....(1)

solving simultaneously, b=6.404m
x=6.060m